Problem: Simplify the expression. $(-7y^{3}+5y^{2}-5y)(2y^{3}-6y)$
Solution: First use the distributive property. $ - 7 y^3 (2 y^3) - 7 y^3 (-6 y) + 5 y^2 (2 y^3) + 5 y^2 (-6 y) - 5 y (2 y^3) - 5 y (-6 y) $ Simplify. $ - 14y^{6} + 42y^{4} + 10y^{5} - 30y^{3} - 10y^{4} + 30y^{2} $ $-14y^{6}+10y^{5}+32y^{4}-30y^{3}+30y^{2}$ Identify like terms. $ {- 14y^{6}} {+ 42y^{4}} {+ 10y^{5}} {- 30y^{3}} {- 10y^{4}} {+ 30y^{2}} $ Add the coefficients. $ { -14y^{6}} {+ 10y^{5}} {+ 32y^{4}} { -30y^{3}} {+ 30y^{2}} $